$\dfrac{d}{dx}[5\sin(x)+x^2]=$
Solution: The expression to differentiate includes $\sin(x)$. Remember that the derivative of $\sin(x)$ is $\cos(x)$. Put another way, $\dfrac{d}{dx}[\sin(x)]=\cos(x)$. $\begin{aligned} &\phantom{=}\dfrac{d}{dx}[5\sin(x)+x^2] \\\\ &=5\dfrac{d}{dx}[\sin(x)]+\dfrac{d}{dx}(x^2) \\\\ &=5\cos(x)+2x \end{aligned}$ In conclusion, $\dfrac{d}{dx}[5\sin(x)+x^2]=5\cos(x)+2x$